A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses

Step-by-step explanation:

Let the speed of cyclist be C and bus be B.

Using the concept of relative speed:-

For incoming bus,speed = B + C

For overtaking bus,speed = B - C

Now,distance travelled b/w 2 incoming bus = (B + C)*4

Now,distance travelled b/w 2 overtaking bus = (B - C)*12

so,

(B + C)*4 = (B - C)*12

or, B=2C

Hence,distance b/w two buses in same direction,d=4*(3/2)B=6 B

Therefore, time gap=d/B=6 minutes

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option